Synchronous Motors: Applications And Working Principle

Synchronous Motors: Applications, Starting Methods & Working Principle

Electrical motors are an electro-mechanical device that converts electrical energy to mechanical energy. Based on the type of input we have classified it into single phase and 3 phase motors.

The most common type of 3 phase motors are synchronous motors and induction motors. When three-phase electric conductors are placed in certain geometrical positions (i.e. in a certain angle from one another) – an electrical field is generated. The rotating magnetic field rotates at a certain speed known as the synchronous speed.

If an electromagnet is present in this rotating magnetic field, the electromagnet is magnetically locked with this rotating magnetic field and rotates with the same speed of rotating field.

This is where the term synchronous motor comes from, as the speed of the rotor of the motor is the same as the rotating magnetic field.

It is a fixed speed motor because it has only one speed, which is synchronous speed. This speed is synchronised with the supply frequency. The synchronous speed is given by:

  • N= The Synchronous Speed (in RPM – i.e. Rotations Per Minute)
  • f = The Supply Frequency (in Hz)
  • p = The number of Poles

Construction of Synchronous Motor

Usually, its construction is almost similar to that of a 3 phase induction motor, except the fact that here we supply DC to the rotor, the reason of which we shall explain later. Now, let us first go through the basic construction of this type of motor. From the above picture, it is clear that how do we design this type of machine. We apply three phase supply to the stator and DC supply to the rotor.

Main Features of Synchronous Motors

  1. Synchronous motors are inherently not self starting. They require some external means to bring their speed close to synchronous speed to before they are synchronized.
  2. The speed of operation of is in synchronism with the supply frequency and hence for constant supply frequency they behave as constant speed motor irrespective of load condition
  3. This motor has the unique characteristics of operating under any electrical power factor. This makes it being used in electrical power factor improvement.

Principle of Operation Synchronous Motor

Synchronous motors are a doubly excited machine, i.e., two electrical inputs are provided to it. Its stator winding which consists of a We provide three-phase supply to three-phase stator winding, and DC to the rotor winding.

The 3 phase stator winding carrying 3 phase currents produces 3 phase rotating magnetic flux. The rotor carrying DC supply also produces a constant flux. Considering the 50 Hz power frequency, from the above relation we can see that the 3 phase rotating flux rotates about 3000 revolutions in 1 min or 50 revolutions in 1 sec.

At a particular instant rotor and stator poles might be of the same polarity (N-N or S-S) causing a repulsive force on the rotor and the very next instant it will be N-S causing attractive force. But due to the inertia of the rotor, it is unable to rotate in any direction due to that attractive or repulsive forces, and the rotor remains in standstill condition. Hence a synchronous motor is not self-starting.

Here we use some mechanical means which initially rotates the rotor in the same direction as the magnetic field to speed very close to synchronous speed. On achieving synchronous speed, magnetic locking occurs, and the synchronous motor continues to rotate even after removal of external mechanical means.

But due to the inertia of the rotor, it is unable to rotate in any direction due to that attractive or repulsive forces, and the rotor remains in standstill condition. Hence a synchronous motor is not self-starting.

Here we use some mechanical means which initially rotates the rotor in the same direction as the magnetic field to speed very close to synchronous speed. On achieving synchronous speed, magnetic locking occurs, and the synchronous motor continues to rotate even after removal of external mechanical means.

Methods of Starting of Synchronous Motor

  1. Motor starting with an external prime Mover: Synchronous motors are mechanically coupled with another motor. It could be either 3 phase induction motor or DC shunt motor. Here, we do not apply DC excitation initially. It rotates at speed very close to its synchronous speed, and then we give the DC excitation. After some time when magnetic locking takes place supply to the external motor is cut off.
  2. Damper winding In this case, the synchronous motor is of salient pole type, additional winding is placed in rotor pole face. Initially, when the rotor is not rotating, the relative speed between damper winding and rotating air gap flux is large and an emf is induced in it which produces the required starting torque. As speed approaches synchronous speed, emf and torque are reduced and finally when magnetic locking takes place; torque also reduces to zero. Hence in this case synchronous motor first runs as three phase induction motor using additional winding and finally it is synchronized with the frequency.

Application of Synchronous Motors

  1. Synchronous motor having no load connected to its shaft is used for power factor improvement. Owing to its characteristics to behave at any electrical power factor, it is used in power system in situations where static capacitors are expensive.
  2. Synchronous motor finds application where operating speed is less (around 500 rpm) and high power is required. For power requirement from 35 kW to 2500 KW, the size, weight and cost of the corresponding three phase induction motor is very high. Hence these motors are preferably used. Ex- Reciprocating pump, compressor, rolling mills etc.

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The conservatism principle is the general concept of recognizing expenses and liabilities as soon as possible when there is uncertainty about the outcome, but to only recognize revenues and assets when they are assured of being received. Thus, when given a choice between several outcomes where the probabilities of occurrence are equally likely, you should recognize that transaction resulting in the lower amount of profit, or at least the deferral of a profit. Similarly, if a choice of outcomes with similar probabilities of occurrence will impact the value of an asset, recognize the transaction resulting in a lower recorded asset valuation.

Under the conservatism principle, if there is uncertainty about incurring a loss, you should tend toward recording the loss. Conversely, if there is uncertainty about recording a gain, you should not record the gain.

The conservatism principle can also be applied to recognizing estimates. For example, if the collections staff believes that a cluster of receivables will have a 2% bad debt percentage because of historical trend lines, but the sales staff is leaning towards a higher 5% figure because of a sudden drop in industry sales, use the 5% figure when creating an allowance for doubtful accounts, unless there is strong evidence to the contrary.

The conservatism principle is the foundation for the lower of cost or market rule, which states that you should record inventory at the lower of either its acquisition cost or its current market value.

The principle runs counter to the needs of taxing authorities, since the amount of taxable income reported tends to be lower when this concept is actively employed; the result is less reported taxable income, and therefore lower tax receipts.

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The conservatism principle is only a guideline. As an accountant, use your best judgment to evaluate a situation and to record a transaction in relation to the information you have at that time. Do not use the principle to consistently record the lowest possible profits for a company.

Similar Terms

The conservatism principle is also known as the conservatism concept or the prudence concept.

Method for the production of fermentation vinegar

A method for the submersed, automatically controlled production of fermentation vinegar from ethanol is conducted in two stages. The installation for accomplishing the method includes one or more pre-fermenters and a product fermenter, in connection with which each pre-fermenter exhibits a volume 1.7 to 3.5 times that of the product fermenter. The terminus of the fermentation is reached in the product fermenter when the dissolved oxygen, indicated by means of an oxygen electrode, rises, at which point the product valve is opened. The product fermenter is evacuated when no more alcohol remainder is present. In the final step the alcohol is therefore completely utilized.

Latest Process Engineering Company SA Patents:

This invention concerns both a method and an installation for the submersed, automatically controlled production of fermentation vinegar from ethanol.

Production proceeds in two stages, there being one or more of the preliminary stage.

An arrangement for the production of fermentation acetic acid is known from Swiss Pat. No. 375,315, which operates in principle with two refining units of similar capacity. After complete evacuation of one of the vessels, accordingly as all of the alcohol is consumed, it will be inoculated with a portion from the second vessel and refilled with fresh mash. The end point of the acidifying is determined as a function of the subsidence of the temperature of the medium.

Another two-stage method, according to DE-PS No. 26 57 330, supplies an acid concentration above 15% acetic acid, with an alcohol content of less than 0.5%. There, the bacteria multiplication and acidifying are to be conducted in a first fermentation phase. In a second fermentation phase the acidifying along with the introduction of the acetic acid bacteria is practically finished. Acetic acid bacteria do not multiply much and hence produce acetic acid very slowly. This influences the economy of the method.

Further disadvantages of the known processes are that with a controlling of the vinegar ejection with regard to the temperature a process variable is used which can be influenced by outside considerations and not simply according to the microbiological process. An additional disadvantage of the methods mentioned is that the utilization of the alcohol in the finishing fermentation step is incomplete.


The object of the invention is therefore to accomplish a method whereby the complete utilization of the alcohol changed into acetic acid is automatically controlled, as well as an installation for the conducting of the method.

This object is achieved through a method in which at the terminus of the fermentation the product valve and the product pump of the product fermenter are controlled by means of an oxygen electrode according to the increase of the dissolved oxygen.

In the course of the fermentation the alcohol content continuously decreases in a final step without the introduction of new substrate, while with constant air supply the dissolved oxygen remains constant up to that point at which the alcohol is consumed completely. The partial pressure (pO.sub.2) of the dissolved oxygen is measured as control parameter for the determination of the end point of the fermentation. This controls the progress of the fermentation, in doing which the process variable thusly is converted so that a relative value from 0% dissolved oxygen will be adhered to at normal productivity. Complete absorption of the introduced oxygen is thus obtained in this phase. In the end phase a relative value from 100% dissolved oxygen will be obtained, so that complete consumption of the oxidizable alcoholic substrate is signified. The increase of the pO.sub.2 -process variable will by means of threshold contact with the range of 70-100% be used for release of the control.

The acidifying ensuing up to the final concentration of the biologically oxidizable ethanol practically signifies an alcoholic remainder of zero. The output stage becomes completely depleted except for remaining alcohol. Thereupon the void fermentation container of the output stage is filled again automatically with a volume portion of the substrate together with the acetic acid bacteria from one or more prefermenters, while new mash is introduced into the pre-fermenter(s). The pre-acidifying ensues up to an alcohol content from 0.5 to 3 percent by volume.

The volume ratio of the prefermenter to the final fermenter amounts to about 1.7 to 3.

The novel features which are considered as characteristic for the invention are set forth in particular in the appended claims. The invention itself, however, both as to its construction and its method of operation, together with additional objects and advantages thereof, will be best understood from the following description of specific embodiments when read in connection with the accompanying drawings.


In the single FIGURE is shown the arrangement for the simplest case of one pre-fermenter A and one product fermenter E.


The pre-fermenter A has 1.7 to 3.5 times the volume of product fermenter E. The two fermenters consist of a container 1 resp. 1′, a central conduit tube 2 resp. 2′, a drive 3 resp. 3′, and a mechanical foam separator 4 resp. 4′. Both containers are provided with hollow body flow checks for stabilizing the temperature, as well as the air supply system 5 resp. 5′. The pre-fermenter A has a substrate supply line 6 which is connected to the feed pump 7. A delivery conduit 8 with valve 11 leads from pre-fermenter A beyond pump 9 to the entry conduit 10 of fermenter E. Fermenter E is provided with a product valve 11′, a conduit 14 and a pump 16. The valve 11′ is controlled by the oxygen-electrode 12 above the amplifier arrangement 13. Both fermenters are equipped with pressure cells 15 resp. 15′ for measuring the container contents.

During operation pre-fermenter A will, to begin with, be pre-acidified up to an alcohol content from 0.5 to 3 percent by volume in known manner. Following that a volume portion will be exacted out of pre-fermenter A across line element 8 through pump 9 and line element 10 to product fermenter E under constant aeration with an air quantity such as is ventilated into pre-fermenter A of 6 m.sup.3 per hour and 1 m.sup.3 working volume, and with the regulated temperature held constant. The measured value of the dissolved oxygen contents is 0% and rises to 100% in the final stage. From that moment the new conveyance to end fermenter E will be conducted by means of a standard controlled terminal based upon a temporarily determined function of the actual desired value comparison of the dissolved pO.sub.2 data, which cuts off so that there does not occur a build-up until constant pO.sub.2 —development for the clearing of the product control. In operation of the mentioned control condition the obtained working volume of the corresponding pre-fermenter must be reported as given across the standard terminal, in order that no final fermenter evacuation can, with disturbances, result, before the pre-fermenter has concluded its substrate conveyance. In the range from 70-100% valve 11′ opens itself, by means of which the contents of fermenter E are conducted through conduit 14 for additional working.

With the approach having two fermenters, the biological system stabilizes itself automatically with no parameter variations; with three fermenters corrections must be undertaken by parameter variations.

By way of a computational example, the equilibrium between partial renewal in the input stage Va and the final stage Ve is presented: ##EQU1##

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The advantages of this method are thereby seen, that the productivity is greater than the sum of the capacities of equally dimensioned single stage fermenters, since in the batch process of the product step active biomass is introduced. By means of the batch process of the product step the oxidizable alcohol will be utilized completely by the acetobacter.

It will be understood that each of the elements described above, or two or more together, may also find a useful application in other types of fermentation productions differing from the types described above.

While the invention has been illustrated and described as embodied in a method and apparatus for the production of fermentation vinegar, it is not intended to be limited to the details shown, since various modifications and structural changes may be made without departing in any way from the spirit of the present invention.

Without further analysis, the foregoing will so fully reveal the gist of the present invention that others can, by applying current knowledge, readily adapt it for various applications without omitting features that, from the standpoint of prior art, fairly constitute essential characteristics of the generic or specific aspects of this invention.


1. In a method for the submersed, automatically controlled production of vinegar from ethanol, of the type in which fermenting is begun by pre-acidifying mash with acetic acid bacteria, the improvement comprising completing fermenting with constant dissolved oxygen content while the alcohol in said mash becomes completely consumed, with constant air supply and without introduction of new substrate; and recovering vinegar at the terminus of fermentation, by means of a product valve controlled through an oxygen electrode, according to increase in dissolved oxygen content.

2. Method according to claim 1, wherein said pre-acidifying ensues up to an alcohol content of about 0.5 to 3 percent by volume.

3. A continuous method for the production of vinegar according to claim 1, further comprising after said recovering vinegar at the terminus of fermentation automatically filling the thereby evacuated fermentation vessel with a volume portion of substrate together with acetic acid bacteria from one or more vessels used for said pre-acidifying.

4. Method according to claim 3, further comprising after said automatically filling said evacuated fermentation vessels automatically refilling said one or more vessels used for said pre-acidifying with fresh mash.

5. Method according to claim 4, wherein said filling and said refilling are controlled through a weight measuring system.

11: Titration of Vinegar (Experiment)

  • Contributed by Santa Monica College
  • ONLINE CHEMISTRY LAB MANUAL at Santa Monica College

To determine the molarity and percent by mass of acetic acid in vinegar.

Vinegar is essentially a solution of acetic acid ((ce)) in water. The concentration of acetic acid in vinegar may be expressed as a molarity (in mol/L):

or as a mass percent

In this experiment, a technique known as a titration will be used to determine the concentration of acetic acid in vinegar. A titration involves performing a controlled reaction between a solution of known concentration (the titrant) and a solution of unknown concentration (the analyte). Here, the titrant is an aqueous solution of

0.1 M sodium hydroxide ((ce)) and the analyte is vinegar. When mixed, a neutralization reaction occurs between sodium hydroxide and the acetic acid in vinegar:

The sodium hydroxide will be gradually added to the vinegar in small amounts from a burette. A burette is a device that allows the precise delivery of a specific volume of a solution. The (ce) will be added to the vinegar sample until all the acetic acid in the vinegar has been exactly consumed (reacted away). At this point the reaction is completed, and no more (ce) is required. This is called the equivalence point of the titration.

In order to know when the equivalence point is reached, an indicator solution called phenolphthalein is added to the vinegar at the beginning of the titration. Phenolphthalein is a pH sensitive organic dye. Phenolphthalein is colorless in acidic solutions like vinegar, and deep pink in basic solutions like sodium hydroxide. At the equivalence point of the titration, just one drop of (ce) will cause the entire solution in the Erlenmeyer flask to change from colorless to a very pale pink.

As the titration is performed, the following data will be collected:

  • The molarity of (ce) (aq) used
  • The volume of (ce) (aq) used to neutralize the vinegar
  • The volume of vinegar used.

Using this data, the molarity and mass percent of acetic acid in vinegar can be determined by performing a series of solution stoichiometry calculations (see Calculations Section).


Materials and Equipment

50-mL burette*, 5-mL volumetric pipette*, pipette bulb*,

0.1 M (ce) (aq), vinegar, phenolphthalein, burette stand, two 250-mL (or 125 mL) Erlenmeyer flasks, wash bottle with distilled water, funnel

Be especially careful when handling the sodium hydroxide base ((ce)), as it is corrosive and can cause chemical burns to the skin. If any NaOH spills on you, rinse immediately under running water for up to 15 minutes and report the accident to your instructor.

Titration Procedure

Your instructor will demonstrate the correct use of the volumetric pipette and burette at the beginning of the lab session. Detailed instructions on how to use a pipette are also found on the last page of this handout. Note that three titrations must be performed.

  1. Obtain a 50-mL burette, 5-mL volumetric pipette and a pipette bulb from the stockroom.

Setting up the burette and preparing the (ce)

  1. Rinse the inside of the burette with distilled water. Allow the distilled water to drain out through the tip in order to ensure that the tip is also rinsed.
  2. Now rinse the burette with a small amount of (ce) (aq). To do this, add about 5-mL of (ce) (aq) to the burette, then twirl the burette on its side (over the sink) to rinse its entire inner surface. Then allow the (ce) (aq) to drain out through the tip.
  3. Fill the burette with (ce) (aq) up to the top, between 0-mL and 5-mL. Use a funnel to do this carefully, below eye-level, and preferably over the sink. After this you will need to flush the tip of the burette – your instructor will show you how to do this. Now measure the volume at the level of the (ce) precisely, and record it as the “Initial Burette Reading” on your report. Also record the exact molarity of the NaOH (aq), which is labeled on the stock bottle.

Preparing the vinegar sample

  1. The volumetric pipette used in this lab is designed to measure and transfer exactly 5.00 mL of solution. First, rinse the inside of the volumetric pipette with distilled water. Using the pipette bulb, draw the water into the pipette up above the 5-mL mark, then allow it to drain out through the tip. You may want to do this several times for practice. Then perform a final rinse, but this time use vinegar.
  2. Now use the volumetric pipette to transfer 5.00-mL of vinegar into a clean 250-mL Erlenmeyer flask (see instructions on page 4). Record this volume of vinegar (precise to two decimal places) on your report. Then add about 20-mL of distilled water and 5 drops of phenolphthalein to this Erlenmeyer flask.

Performing the titration

  1. Begin the titration by slowly adding (ce) (aq) from the burette to the vinegar in the Erlenmeyer flask. Swirl Erlenmeyer flask as you add the base in order to efficiently mix the chemicals. Some pinkness may appear briefly in the flask as the base is added, but it will quickly disappear as the flask is swirled.
  2. As the equivalence point is approached, the pink color will become more pervasive and will take longer to disappear. When this occurs, start to add the (ce) (aq) drop by drop. Eventually the addition of just one drop of (ce) (aq) will turn the solution in the Erlenmeyer flask a pale pink color that does not disappear when swirled. This indicates that the equivalence point has been reached. Do not add any more (ce) (aq) at this point. Measure this volume of (ce) (aq) precisely, and record it as the “Final Burette Reading” on your report. Then show the resulting solution in the flask to your instructor so s/he can record the final color on your report form.
  3. Refill your burette with (ce) (aq), and then repeat this procedure for a second sample of vinegar, and then a third sample of vinegar. You do not need to flush the tip of the burette again. Note that if you use less than 25-mL of (ce) (aq) for the second titration, you do not need to refill the burette for the third titration; also that you will need to clean out and re-use one of your Erlenmeyer flasks for the third titration. You and your partner should take turns performing these titrations.
  4. When finished, dispose of your chemical waste as instructed.

Pipetting Instructions

  1. Get the appropriate amount of the solution you wish to pipette in a clean, dry beaker. Never pipette directly out of the stock bottles of solution. This creates a contamination risk.
  2. Insert the tip of the pipette into the beaker of solution so that it is about a quarter inch from the bottom. Be sure not to press the tip against the bottom of the container.
  3. If you are right handed, hold the pipette in your right hand, leaving your index finger free to place over the top of the pipette. With your left hand, squeeze the pipette bulb. Press it firmly over the top of the pipette, but DO NOT INSERT THE PIPET DEEP INTO THE BULB!
  4. Release the pressure on the bulb and allow the solution to be drawn up into the pipette until it is above the volume mark. Do not allow the solution to be sucked into the bulb itself.
  5. Quickly remove the bulb and place your index finger firmly over the top of the pipette. Then remove the pipette tip from the beaker of solution.
  6. Slowly roll your finger to one side and allow the liquid to drain until the bottom of the meniscus is aligned with the volume mark. With practice you will be able to lower the liquid very, very slowly.
  7. When the bottom of the meniscus is even with the volume mark, press your index finger firmly on the top of the pipette so no liquid leaks out. Touch the tip once to the side of the beaker to remove any hanging drops.
  8. To transfer the solution, place the tip of the pipette against the wall of the receiving container at a slight angle. Then allow the liquid to drain from the pipette.
  9. When the solution stops flowing, touch the pipette once to the side of the receiving container to remove any hanging drops. DO NOT blow out the remaining solution. The pipette has been calibrated to deliver the appropriate amount of solution with some remaining in the tip.


Molarity of Acetic Acid in Vinegar

  • First, using the known molarity of the (ce) (aq) and the volume of (ce) (aq) required to reach the equivalence point, calculate the moles of (ce) used in the titration.
  • From this mole value (of (ce)), obtain the moles of (ce) in the vinegar sample, using the mole-to-mole ratio in the balanced equation.
  • Finally, calculate the molarity of acetic acid in vinegar from the moles of (ce) and the volume of the vinegar sample used.

Mass Percent of Acetic Acid in Vinegar

  • First, convert the moles of (ce) in the vinegar sample (previously calculated) to a mass of (ce), via its molar mass.
  • Then determine the total mass of the vinegar sample from the vinegar volume and the vinegar density. Assume that the vinegar density is 1.000 g/mL (= to the density of water).
  • Finally, calculate the mass percent of acetic acid in vinegar from the mass of (ce) and the mass of vinegar.

Pre-laboratory Assignment: Titration of Vinegar

  1. In this lab, you will perform a titration using sodium hydroxide and acetic acid (in vinegar). Write the balanced neutralization reaction that occurs between sodium hydroxide and acetic acid.
  1. Specialized equipment is needed to perform a titration.
  • Consider the sodium hydroxide reactant.
    • Name the specialized device the sodium hydroxide is placed in.
    • Is the concentration of the sodium hydroxide known or unknown?
    • Is sodium hydroxide the analyte or the titrant?
  • Consider the acetic acid reactant.
    • What type of flask is the acetic acid placed in?
    • What volume of acetic acid is used?
    • What specialized device is used to obtain this precise volume?
    • Is the acetic acid the analyte or the titrant?
  1. You will add sodium hydroxide to the acetic acid until all the acetic acid is consumed. This is a special point in the titration called the _________________________ point.
  2. An indicator solution is used to indicate when all the acetic acid has been consumed and that the reaction in complete.
  • What is the name of the indicator solution?
  • Is this indicator mixed with sodium hydroxide or acetic acid?
  • How exactly does the indicator let you know when the reaction is complete?

Lab Report: Titration of Vinega r

Experimental Data

Trial 1

Trial 2

Trial 3

Initial Buret Reading

Final Buret Reading

Volume of (ce) (aq) used

Molarity of (ce) (aq) used

Volume of Vinegar used

Color at equivalence point – to be recorded by your instructor

Data Analysis

Write the balanced equation for the neutralization reaction between aqueous sodium hydroxide and acetic acid.

The Molarity of Acetic Acid in Vinegar

Use your two best sets of results (with the palest pink equivalence points) along with the balanced equation to determine the molarity of acetic acid in vinegar. Show all work for each step in the spaces provided.

Data used ⇒

Trial _____

Trial _____

Moles of (ce) used in titration

Moles of (ce) neutralized in vinegar sample

Molarity of (ce) in vinegar

The Mass Percent of Acetic Acid in Vinegar

Use your two best sets of results along with calculated values in the previous table to determine the mass percent of acetic acid in vinegar. Show all work for each step in the spaces provided.

Data used ⇒

Trial _____

Trial _____

Mass of (ce) in vinegar sample

Mass of vinegar sample (assume density = 1.00 g/mL)

Mass Percent of (ce) in vinegar

Average Mass Percent

  1. What was the purpose of the phenolphthalein indicator in this experiment? Be specific.
  1. Suppose you added 40 mL of water to your vinegar sample instead of 20 mL. Would the titration have required more, less or the same amount of (ce) (aq) for a complete reaction? Explain.
  1. Consider a 0.586 M aqueous solution of barium hydroxide, (ce) (aq).
  • How many grams of (ce) are dissolved in 0.191 dL of 0.586 M (ce) (aq)?
  • How many individual hydroxide ions ((ce>)) are found in 13.4 mL of 0.586 M (ce) (aq)?
  • What volume (in L) of 0.586 M (ce) (aq) contains 0.466 ounces of (ce) dissolved in it?
  1. If 16.0 mL of water are added to 31.5 mL of 0.586 M (ce) (aq), what is the new solution molarity?
  2. Suppose you had titrated your vinegar sample with barium hydroxide instead of sodium hydroxide:
  • What volume (in mL) of 0.586 M (ce) (aq) must be added to a 5.00 mL sample of vinegar to reach the equivalence point? Use your average vinegar molarity (see page 1) in this calculation.

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